Jan Carl Budich: Obstructions to Quantum State Preparation: From Topology to Computational Complexity

The complexity of the quantum many-body problem is well known to be fully reflected in the generally hard task of quantum state preparation. In this talk, we discuss the critical slowdown of dissipative state preparation protocols due to two fundamental obstructions: topological quantum phase transitions and the computational complexity of combinatorial problems the solution to which is encoded in the targeted quantum many-body state. Specifically, we relate the complexity of a given obstruction directly to the finite size scaling of the dissipative dynamics. Finally, we discuss implications on realizing or simulating state preparation protocols both on classical and quantum devices.